Collaboration diagram for Curves:

Classes
class	MbArc3D
	Elliptical arc in three-dimensional space. More...

class	MbBSpline
	B-spline set of NURBS-curve. More...

class	MbBezier3D
	Bezier spline in three-dimensional space. More...

class	MbBridgeCurve3D
	Bridge curve connecting ends of two curves. More...

class	MbCharacterCurve3D
	Functionally defined curve. More...

class	MbConeSpiral
	Conical spiral. More...

class	MbContour3D
	Contour in three-dimensional space. More...

class	MbContourOnPlane
	Contour on plane. More...

class	MbContourOnSurface
	Contour on surface. More...

class	MbCrookedSpiral
	Spiral with a curvilinear axis. More...

class	MbCubicSpline3D
	Cubic spline. More...

class	MbCurveSpiral
	Spiral with a variable radius. More...

class	MbHermit3D
	Composite Hermite cubic spline in three-dimensional space. More...

class	MbLine3D
	Line in three-dimensional space. More...

class	MbLineSegment3D
	Line segment in three-dimensional space. More...

class	MbNurbs3D
	NURBS curve in three-dimensional space. More...

class	MbOffsetCurve3D
	Offset curve in three-dimensional space. More...

class	MbPlaneCurve
	Plane curve in three-dimensional space. More...

class	MbPolyCurve3D
	Curve in three-dimensional space, defined by points. More...

class	MbPolyline3D
	Polyline in three-dimensional space. More...

class	MbReparamCurve3D
	Reparametrized curve in three-dimensional space. More...

class	MbSilhouetteCurve
	Isocline curve or silhouette curve of surface. More...

class	MbSpiral
	Spiral. More...

class	MbSurfaceCurve
	Curve on surface. More...

class	MbSurfaceIntersectionCurve
	Intersection curve of two surfaces. More...

class	MbTrimmedCurve3D
	Trimmed curve in three-dimensional space. More...

class	MbCurve3D
	Curve in three-dimensional space. More...

Functions
MbCurve3D *	TrimContour (const MbContour3D &cntr, double t1, double t2, int sense, bool useTrimmedOnly, bool saveParamLenAndLaw=false)
	Trim a contour. More...

MbeNewtonResult	NearestPoints (const MbCurve3D &curve1, bool ext1, const MbCurve3D &curve2, bool ext2, double &t1, double &t2, double &dmin)
	Calculate parameters of the nearest points of two curves. More...

MbeNewtonResult	CurveCrossNewton (const MbCurve3D &curve1, bool ext1, const MbCurve3D &curve2, bool ext2, double funcEpsilon, size_t iterLimit, double &t1, double &t2, bool correctNewtonParam=true)
	Definition of parameters of the nearest points of curves. More...

void	CalculatePolygon (const MbCurve3D &curve, const MbStepData &stepData, std::vector< std::pair< double, MbCartPoint3D > > &paramPoints)
	Calculate polygon points of curve. More...

Functions for working inside and outside the curve's domain.
Functions _PointOn, _FirstDer, _SecondDer, _ThirdDer,... do not correct parameter when it is out of domain bounds. When parameter is out of domain bounds, an unclosed curve is extended by tangent vector at corresponding end point in general case. The exceptions are arcs of ellipse and arcs of circle - they are extended according to their equations.
virtual void	MbCurve::Explore (double &t, bool ext, MbCartPoint &pnt, MbVector &fir, MbVector sec, MbVector thir) const
	Calculate point and derivatives of object for given parameter. More...

Functions for curve domain description
virtual bool	MbCurve3D::IsClosed () const =0
	Define whether the curve is periodic. More...

virtual bool	MbCurve3D::IsPeriodic () const
	Define whether the curve is periodic. More...

Functions for working in the curve's domain.\n
functions PointOn, FirstDer, SecondDer, ThirdDer,... correct parameter when it is out of domain bounds. The exception is MbLine3D (line).
virtual void	MbCurve3D::PointOn (double &t, MbCartPoint3D &p) const =0
	Calculate a point on the curve. More...

virtual void	MbCurve3D::FirstDer (double &t, MbVector3D &) const =0
	Calculate first derivative.

virtual void	MbCurve3D::SecondDer (double &t, MbVector3D &) const =0
	Calculate second derivative.

virtual void	MbCurve3D::ThirdDer (double &t, MbVector3D &) const =0
	Calculate third derivative.

virtual void	MbCurve3D::Tangent (double &t, MbVector3D &) const
	Calculate tangent vector (normalized).

virtual void	MbCurve3D::Normal (double &t, MbVector3D &) const
	Calculate main normal vector.

virtual void	MbCurve3D::BNormal (double &t, MbVector3D &) const
	Calculate binormal vector.

Functions for working inside and outside the curve's domain\n
functions _PointOn, _FirstDer, _SecondDer, _ThirdDer,... do not correct parameter when it is out of domain bounds.
virtual void	MbCurve3D::_PointOn (double t, MbCartPoint3D &p) const
	Calculate point at curve and its extension. More...

virtual void	MbCurve3D::Explore (double &t, bool ext, MbCartPoint3D &pnt, MbVector3D &fir, MbVector3D sec, MbVector3D thir) const
	Calculate point and derivatives of object for given parameter. More...

virtual void	MbCurve3D::FastApproxExplore (double &t, MbCartPoint3D &pnt, MbVector3D &fir, MbVector3D *sec) const
	Calculate point and derivatives on the curve. More...

virtual void	MbCurve3D::_FirstDer (double t, MbVector3D &) const
	Calculate first derivative at curve and its extension.

virtual void	MbCurve3D::_SecondDer (double t, MbVector3D &) const
	Calculate second derivative at curve and its extension.

virtual void	MbCurve3D::_ThirdDer (double t, MbVector3D &) const
	Calculate third derivative at curve and its extension.

virtual void	MbCurve3D::_Tangent (double t, MbVector3D &) const
	Calculate tangent vector (normalized) at curve and its extension.

virtual void	MbCurve3D::_Normal (double t, MbVector3D &) const
	Calculate main normal vector (normalized) at curve and its extension.

virtual void	MbCurve3D::_BNormal (double t, MbVector3D &) const
	Calculate binormal vector (normalized) at curve and its extension.

Function of moving by curve
virtual double	MbCurve3D::Step (double t, double sag) const
	Calculate parameter step. More...

virtual double	MbCurve3D::DeviationStep (double t, double ang) const
	Calculate parameter step. More...

virtual double	MbCurve3D::MetricStep (double t, double length) const
	Calculate parameter step. More...

double	MbCurve3D::CurveStep (const double &t, const MbStepData &stepData) const
	Calculate parameter step. More...

Common function of curve.
virtual MbCurve3D *	MbCurve3D::NurbsCurve (const MbNurbsParameters &tParameters) const
	Construct a NURBS copy of a curve. More...

virtual MbCurve3D *	MbCurve3D::Trimmed (double t1, double t2, int sense, bool saveParamLenAndLaw=false) const
	Construct a trimmed curve. More...

virtual MbCurve3D *	MbCurve3D::Trimmed (double t1, double t2, int sense, const MbDimAccuracy &xyzEps, bool saveParamLenAndLaw) const
	Construct a trimmed curve with the given two-dimensional accuracy. More...

virtual double	MbCurve3D::CalculateLength (double t1, double t2) const
	Calculate the metric length of a curve. More...

virtual bool	MbCurve3D::DistanceAlong (double &t, double len, int curveDir, double eps=Math::metricPrecision, VERSION version=Math::DefaultMathVersion()) const
	Translate parameter along the curve. More...

virtual bool	MbCurve3D::ChangeCarrierBorne (const MbSpaceItem &item, MbSpaceItem &init, const MbMatrix &matr)
	Change the carrier. More...

virtual void	MbCurve3D::CalculatePolygon (const MbStepData &stepData, MbPolygon3D &polygon) const
	Calculate an array of points for drawing. More...

virtual MbeNewtonResult	MbCurve3D::PointProjectionNewton (const MbCartPoint3D &p, size_t iterLimit, double &t, bool ext) const
	Find the point projection to the curve. More...

virtual bool	MbCurve3D::NearPointProjection (const MbCartPoint3D &pnt, double &t, bool ext, MbRect1D *tRange=nullptr) const
	Find the point projection to the curve. More...

virtual MbeNewtonResult	MbCurve3D::IsoclinalNewton (const MbVector3D &dir, size_t iterLimit, double &t) const
	Find isoclines of a curve. More...

virtual void	MbCurve3D::GetIsoclinal (const MbVector3D &nor, SArray< double > &tIso) const
	Find all isoclines of a curve. More...

virtual MbCurve *	MbCurve3D::GetMap (const MbMatrix3D &into, MbRect1D pRegion=nullptr, VERSION version=Math::DefaultMathVersion(), bool coincParams=nullptr) const
	Construct a planar projection of a piece of a space curve. More...

virtual MbCurve *	MbCurve3D::GetMapPsp (const MbMatrix3D &into, double zNear, MbRect1D *pRegion=nullptr) const
	Construct a planar projection of a piece of a space curve. More...

virtual MbCurve *	MbCurve3D::GetProjection (const MbPlacement3D &place, VERSION version) const
	Construct a planar projection of a space curve to a plane. More...

bool	MbCurve3D::IsSpaceNear (const MbCurve3D &curve, double eps, bool ext, double devSag=5.0 *Math::deviateSag) const
	Check whether the two curves are metrically close. More...

virtual void	MbCurve3D::GetCurvatureSpecialPoints (std::vector< c3d::DoublePair > &points) const
	Find all the special points of the curvature function of the curve. More...

virtual void	MbCurve3D::GetAnalyticalFunctionsBounds (std::vector< double > &params) const
	Get the boundaries of the curve sections that are described by one analytical function. More...

MbCartPoint3D	MbCurve3D::GetLimitPoint (ptrdiff_t number) const
	Calculate the boundary point. More...

void	MbCurve3D::GetLimitPoint (ptrdiff_t number, MbCartPoint3D &pnt) const
	Calculate the boundary point. More...

Common functions
virtual void	MbFunction::Explore (double &t, bool ext, double &val, double &fir, double sec, double thr) const
	Calculate value and derivatives of object for given parameter. More...

Detailed Description

Function Documentation

◆ TrimContour()

MbCurve3D* TrimContour	(	const MbContour3D &	cntr,
		double	t1,
		double	t2,
		int	sense,
		bool	useTrimmedOnly,
		bool	saveParamLenAndLaw = `false`
	)

Trim a contour.

Trim a contour. This function is extended version of contour's function Trimmed.

Parameters

[in]	t1	- Parameter corresponding to start of a trimmed curve.
[in]	t2	- Parameter corresponding to end of a trimmed curve.
[in]	sense	- Direction of a trimmed curve in relation to an initial curve. sense = 1 - direction does not change. sense = -1 - direction changes to the opposite value.
[in]	useTrimmedOnly	- A truncated segment is always curve MbTrimmedCurve3D.

Returns: A constructed trimmed curve.

◆ Explore() [1/3]

virtual void MbCurve::Explore	(	double &	t,
		bool	ext,
		MbCartPoint &	pnt,
		MbVector &	fir,
		MbVector *	sec,
		MbVector *	thir
	)		const

virtual

Calculate point and derivatives of object for given parameter.

Values of point and derivatives are calculated on parameter area and on extended curve.

Parameters

[in]	t	- Parameter.
[in]	ext	- On parameters area (false), on extended curve (true).
[out]	pnt	- Point.
[out]	fir	- Derivative with respect to t.
[out]	sec	- Second derivative with respect to t, if not nullptr.
[out]	thir	- Third derivative with respect to t, if not nullptr.

Reimplemented in MbTrimmedCurve, MbReparamCurve, MbProjCurve, MbPolyline, MbPointCurve, MbOffsetCurve, MbNurbs, MbLineSegment, MbLine, MbHermit, MbCubicSpline, MbCosinusoid, MbContour, MbCharacterCurve, MbBezier, and MbArc.

◆ IsClosed()

virtual bool MbCurve3D::IsClosed ( ) const

pure virtual

Define whether the curve is periodic.

Define whether the curve is periodic.
A periodic curve is closed. A curve is considered as periodic if:

start point is coincident with end point;
derivatives in start point and end point coincide;
if there are breaks at curve (in cases when a curve is contour or polyline), then derivatives may not coincide; in Bezier curve derivatives should coincide by direction, but they may differ by absolute value.
Curves:
MbLine3D,
MbLineSegment3D,
MbSpiral and inherited classes,
MbBridgeCurve3D,
MbContour3D (if it contains only a single segment of one of the listed types)
are not considered periodic when the start and end points coincide. The IsClosed() method always returns false for them.
Returns
True if a curve is closed.

Implemented in MbTrimmedCurve3D, MbSurfaceIntersectionCurve, MbSurfaceCurve, MbSpiral, MbReparamCurve3D, MbPolyCurve3D, MbPlaneCurve, MbOffsetCurve3D, MbNurbs3D, MbLineSegment3D, MbLine3D, MbCrookedSpiral, MbContourOnSurface, MbContour3D, MbCharacterCurve3D, MbBridgeCurve3D, MbBSpline, and MbArc3D.

◆ IsPeriodic()

virtual bool MbCurve3D::IsPeriodic ( ) const

virtual

Define whether the curve is periodic.

Define whether the curve is periodic.
A curve is considered as periodic if:

start point is coincident with end point;
derivatives in start point and end point coincide;
if there are breaks at curve (in cases when a curve is contour or polyline), then derivatives may not coincide; in Bezier curve derivatives should coincide by direction, but they may differ by absolute value.
Curves:
MbLine3D,
MbLineSegment3D,
MbSpiral and inherited classes,
MbBridgeCurve3D,
MbContour3D (if it contains only a single segment of one of the listed types)
are not considered periodic when the start and end points coincide. The IsPeriodic() method always returns false for them.
Returns
True if a curve is closed.

Reimplemented in MbSurfaceIntersectionCurve, and MbNurbs3D.

◆ PointOn()

virtual void MbCurve3D::PointOn	(	double &	t,
		MbCartPoint3D &	p
	)		const

pure virtual

Calculate a point on the curve.

Correct parameter when getting out of domain bounds and calculate a point on the curve.

Parameters

[in]	t	- Curve parameter.
[out]	p	- A point on the curve.

Implemented in MbCurveSpiral, MbCrookedSpiral, MbConeSpiral, MbBSpline, MbOffsetCurve3D, MbTrimmedCurve3D, MbSurfaceIntersectionCurve, MbSurfaceCurve, MbSilhouetteCurve, MbReparamCurve3D, MbPolyline3D, MbPlaneCurve, MbNurbs3D, MbLineSegment3D, MbLine3D, MbHermit3D, MbContourOnSurface, MbContourOnPlane, MbContour3D, MbCharacterCurve3D, MbBridgeCurve3D, MbBezier3D, MbArc3D, and MbCubicSpline3D.

◆ _PointOn()

virtual void MbCurve3D::_PointOn	(	double	t,
		MbCartPoint3D &	p
	)		const

virtual

Calculate point at curve and its extension.

Calculate a point on the curve including the outside area determination parameter.

Parameters

[in]	t	- Curve parameter.
[out]	p	- A point on the curve.

Reimplemented in MbCurveSpiral, MbCrookedSpiral, MbConeSpiral, MbHermit3D, MbTrimmedCurve3D, MbSurfaceIntersectionCurve, MbSurfaceCurve, MbSilhouetteCurve, MbReparamCurve3D, MbPlaneCurve, MbLineSegment3D, MbLine3D, MbContourOnSurface, MbContourOnPlane, MbContour3D, and MbArc3D.

◆ Explore() [2/3]

virtual void MbCurve3D::Explore	(	double &	t,
		bool	ext,
		MbCartPoint3D &	pnt,
		MbVector3D &	fir,
		MbVector3D *	sec,
		MbVector3D *	thir
	)		const

virtual

Calculate point and derivatives of object for given parameter.

Values of point and derivatives are calculated on parameter area and on extended curve.

Parameters

[in]	t	- Parameter.
[in]	ext	- On parameters area (false), on extended curve (true).
[out]	pnt	- Point.
[out]	fir	- Derivative with respect to t.
[out]	sec	- Second derivative with respect to t, if not nullptr.
[out]	thir	- Third derivative with respect to t, if not nullptr.

Reimplemented in MbTrimmedCurve3D, MbSurfaceIntersectionCurve, MbSurfaceCurve, MbSilhouetteCurve, MbReparamCurve3D, MbPolyline3D, MbPlaneCurve, MbOffsetCurve3D, MbNurbs3D, MbLineSegment3D, MbLine3D, MbHermit3D, MbCurveSpiral, MbCubicSpline3D, MbCrookedSpiral, MbContourOnSurface, MbContourOnPlane, MbContour3D, MbConeSpiral, MbCharacterCurve3D, MbBridgeCurve3D, MbBezier3D, MbBSpline, and MbArc3D.

◆ FastApproxExplore()

virtual void MbCurve3D::FastApproxExplore	(	double &	t,
		MbCartPoint3D &	pnt,
		MbVector3D &	fir,
		MbVector3D *	sec
	)		const

virtual

Calculate point and derivatives on the curve.

The function is overloaded in MbSurfaceIntersectionCurve and MbSilhouetteCurve for the fast approximated calculation of a point and derivatives. In other surfaces it is equivalent to the function Explore(t,false,pnt,fir,sec,nullptr).

Parameters

[in]	t	- Parameter.
[out]	pnt	- A calculated point.
[out]	fir	- Derivative with respect to t.
[out]	sec	- Second derivative with respect to t, if not nullptr.

Reimplemented in MbSurfaceIntersectionCurve, and MbSilhouetteCurve.

◆ Step()

virtual double MbCurve3D::Step	(	double	t,
		double	sag
	)		const

virtual

Calculate parameter step.

Calculate parameter step for the curve's approximation by its sag value. Calculation of the step is performed with consideration of curvature radius. A step of curve's approximation is chosen in such way, that the deviation from its polygon does not exceed the given value of sag.

Parameters

[in]	t	- A parameter defining the point on a curve, at which a step should be calculated.
[in]	sag	- Maximum feasible sag value.

Returns: A sag value by parameter at given point.

Reimplemented in MbTrimmedCurve3D, MbSurfaceIntersectionCurve, MbSurfaceCurve, MbSpiral, MbReparamCurve3D, MbPolyline3D, MbPlaneCurve, MbOffsetCurve3D, MbNurbs3D, MbLineSegment3D, MbLine3D, MbHermit3D, MbCubicSpline3D, MbContourOnSurface, MbContourOnPlane, MbContour3D, MbConeSpiral, MbCharacterCurve3D, MbBridgeCurve3D, MbBezier3D, MbBSpline, and MbArc3D.

◆ DeviationStep()

virtual double MbCurve3D::DeviationStep	(	double	t,
		double	ang
	)		const

virtual

Calculate parameter step.

Calculate parameter step for the curve's approximation by the deviation angle of the tangent vector. A step of curve's approximation is chosen in such way, that angular deviation of the tangent curve at the next point does not exceed the given value ang.

Parameters

[in]	t	- A parameter defining the point on a curve, at which a step should be calculated.
[in]	ang	- The maximum feasible deviation angle of tangent.

Returns: A sag value by parameter at given point.

Reimplemented in MbContourOnPlane, MbTrimmedCurve3D, MbSurfaceIntersectionCurve, MbSurfaceCurve, MbSpiral, MbSilhouetteCurve, MbReparamCurve3D, MbPolyline3D, MbPlaneCurve, MbOffsetCurve3D, MbNurbs3D, MbLineSegment3D, MbLine3D, MbHermit3D, MbCubicSpline3D, MbContourOnSurface, MbContour3D, MbConeSpiral, MbBridgeCurve3D, MbBezier3D, MbArc3D, and MbCharacterCurve3D.

◆ MetricStep()

virtual double MbCurve3D::MetricStep	(	double	t,
		double	length
	)		const

virtual

Calculate parameter step.

Calculate the parameter step for approximation of a curve by the given metric length of a step along a curve.

Parameters

[in]	t	- A parameter defining the point on a curve, at which a step should be calculated.
[in]	len	- Maximum metric length of a step along a curve.

Returns: A sag value by parameter at given point.

Reimplemented in MbTrimmedCurve3D, MbSurfaceIntersectionCurve, MbSurfaceCurve, MbReparamCurve3D, MbPlaneCurve, MbLineSegment3D, MbLine3D, MbContour3D, MbConeSpiral, and MbArc3D.

◆ CurveStep()

double MbCurve3D::CurveStep	(	const double &	t,
		const MbStepData &	stepData
	)		const

Calculate parameter step.

Calculate parameter step for the curve approximation: by diviation sngle; or by its sag value; or by the metric length.

Parameters

[in]	t	- A parameter defining the point on a curve, at which a step should be calculated.
[in]	stepData	- Data for step calculation.

Returns: A sag value by parameter at given point.

◆ NurbsCurve()

virtual MbCurve3D* MbCurve3D::NurbsCurve ( const MbNurbsParameters & tParameters ) const

virtual

Construct a NURBS copy of a curve.

Constructs a NURBS curve which approximates a given curve with the given parameters. In parameters the degree and the number of knots of a spline and the range of curve's parameters changing may be set. If the flag of accurate approximation is not set in parameters then NURBS without multiple knots is constructed.

Parameters

[in] tParameters - Parameters for the construction of a NURBS copy of the curve.

Returns: The constructed NURBS curve or nullptr in a case of failure.

Reimplemented in MbTrimmedCurve3D, MbReparamCurve3D, MbPolyline3D, MbPlaneCurve, MbNurbs3D, MbLineSegment3D, MbLine3D, MbHermit3D, MbCubicSpline3D, MbBridgeCurve3D, MbBezier3D, and MbArc3D.

◆ Trimmed() [1/2]

virtual MbCurve3D* MbCurve3D::Trimmed	(	double	t1,
		double	t2,
		int	sense,
		bool	saveParamLenAndLaw = `false`
	)		const

virtual

Construct a trimmed curve.

Constructs a trimmed curve, a start point of which corresponds to a point with parameter t1 and an end point corresponds to a point with parameter t2. Direction of the constructed curve relative to the initial curve may be changed by the parameter 'sense'. If the curve is closed, then there may be obtained a trimmed curve, passing through the start of a curve.
In a case of closed or periodic curve three parameters 'sense', t1 and t2 clearly define the result. In a case of unclosed curve the parameter 'sense' and parameter of trimming should correspond each other:
1) if sense == 1, then t1 < t2,
2) if sense == -1, then t1 > t2,
If there is a discrepancy between 'sense' and parameters of trimming, then 'sense' parameter has higher priority. If parameters t1 and t2 are equal and the curve is closed, then in result a closed curve should be obtained.

Parameters

[in]	t1	- Parameter corresponding to start of a trimmed curve.
[in]	t2	- Parameter corresponding to end of a trimmed curve.
[in]	sense	- Direction of a trimmed curve in relation to an initial curve. sense = 1 - direction does not change. sense = -1 - direction changes to the opposite value.
[in]	saveParLenAndLaw	- Save parametric length and law.

Returns: A constructed trimmed curve.

◆ Trimmed() [2/2]

virtual MbCurve3D* MbCurve3D::Trimmed	(	double	t1,
		double	t2,
		int	sense,
		const MbDimAccuracy &	xyzEps,
		bool	saveParamLenAndLaw
	)		const

virtual

Construct a trimmed curve with the given two-dimensional accuracy.

Constructs a trimmed curve, a start point of which corresponds to a point with parameter t1 and an end point corresponds to a point with parameter t2. Direction of the constructed curve relative to the initial curve may be changed by the parameter 'sense'. If the curve is closed, then there may be obtained a trimmed curve, passing through the start of a curve.
In a case of closed or periodic curve three parameters 'sense', t1 and t2 clearly define the result. In a case of unclosed curve the parameter 'sense' and parameter of trimming should correspond each other:
1) if sense == 1, then t1 < t2,
2) if sense == -1, then t1 > t2,
If there is a discrepancy between 'sense' and parameters of trimming, then 'sense' parameter has higher priority. If parameters t1 and t2 are equal and the curve is closed, then in result a closed curve should be obtained.

Parameters

[in]	t1	- Parameter corresponding to start of a trimmed curve.
[in]	t2	- Parameter corresponding to end of a trimmed curve.
[in]	sense	- Direction of a trimmed curve in relation to an initial curve. sense = 1 - direction does not change. sense = -1 - direction changes to the opposite value.
[in]	xyzEps	- Three-dimensional accuracy.
[in]	saveParLenAndLaw	- Save parametric length and law.

Returns: A constructed trimmed curve.

Warning: Under development.

Reimplemented in MbTrimmedCurve3D, MbSurfaceIntersectionCurve, MbSurfaceCurve, MbSilhouetteCurve, MbReparamCurve3D, MbPolyline3D, MbPlaneCurve, MbNurbs3D, MbLineSegment3D, MbLine3D, MbHermit3D, MbCurveSpiral, MbCubicSpline3D, MbCrookedSpiral, MbContourOnSurface, MbContourOnPlane, MbContour3D, MbConeSpiral, MbBezier3D, and MbArc3D.

◆ CalculateLength()

virtual double MbCurve3D::CalculateLength	(	double	t1,
		double	t2
	)		const

virtual

Calculate the metric length of a curve.

Calculate the metric length of unclosed curve from parameter t1 to parameter t2. The condition t1 < t2 should satisfied.

Parameters

[in]	t1	- Start parameter of a curve section.
[in]	t2	- End parameter of a curve section.

Returns: Length of a curve.

Reimplemented in MbSurfaceIntersectionCurve, MbReparamCurve3D, MbPlaneCurve, MbNurbs3D, MbLineSegment3D, MbCrookedSpiral, MbContour3D, and MbConeSpiral.

◆ DistanceAlong()

virtual bool MbCurve3D::DistanceAlong	(	double &	t,
		double	len,
		int	curveDir,
		double	eps = `Math::metricPrecision`,
		VERSION	version = `Math::DefaultMathVersion()`
	)		const

virtual

Translate parameter along the curve.

Translate parameter along the curve by the given distance at the given direction. The new value of parameter is saved in the variable t. If the curve is not closed and the length of its part from the point with parameter t to the end at the given direction is less than the required shift, then calculations are performed on extension of the curve, if it possible to construct such extension.

Parameters

[in,out]	t	- Input - the initial value of parameter. Output - the new value of parameter.
[in]	len	- The value of shift along the curve.
[in]	curveDir	- The offset direction. If curveDir is non-negative, then the shift is directed to the side of increasing of parameter. Otherwise - to the side of decreasing of parameter.
[in]	eps	- Computational tolerance.

Returns: True - if the operation is performed successfully, otherwise false.

Reimplemented in MbSurfaceIntersectionCurve, MbReparamCurve3D, MbPlaneCurve, MbNurbs3D, MbLineSegment3D, MbLine3D, MbHermit3D, MbCubicSpline3D, MbContour3D, MbBezier3D, and MbArc3D.

◆ ChangeCarrierBorne()

virtual bool MbCurve3D::ChangeCarrierBorne	(	const MbSpaceItem &	item,
		MbSpaceItem &	init,
		const MbMatrix &	matr
	)

virtual

Change the carrier.

For surface curves. Replaces the current carrier 'item' by a new one, if this is possible. Transforms a carried element by the given matrix.

Parameters

[in]	item	- An initial carrier.
[in]	init	- A new carrier.
[in]	matr	- A matrix for transformation of a carried element.

Returns: True - if the operation is performed successfully, otherwise false.

Reimplemented in MbSurfaceIntersectionCurve, MbContourOnSurface, and MbSurfaceCurve.

◆ CalculatePolygon() [1/2]

virtual void MbCurve3D::CalculatePolygon	(	const MbStepData &	stepData,
		MbPolygon3D &	polygon
	)		const

virtual

Calculate an array of points for drawing.

Get an array of drawn points with a given sag. If the cure is a contour then knots of a contour are duplicated.

Parameters

[in]	stepData	- Data for step calculation.
[in,out]	polygon	- A polygon of calculated points on a curve.

Reimplemented in MbSurfaceIntersectionCurve, MbReparamCurve3D, MbLineSegment3D, and MbLine3D.

◆ PointProjectionNewton()

virtual MbeNewtonResult MbCurve3D::PointProjectionNewton	(	const MbCartPoint3D &	p,
		size_t	iterLimit,
		double &	t,
		bool	ext
	)		const

virtual

Find the point projection to the curve.

Find the point projection to the curve or its extension by the Newton method with the given initial approximation.

Parameters

[in]	p	- A given point.
[in]	iterLimit	- The maximum number of iterations.
[out]	t	- Input - initial approximation, output - parameter of a curve corresponding to the nearest projection.
[in]	ext	- A flag defining whether to seek projection on the extension of the curve.

Returns: The result of the iterative method.

◆ NearPointProjection()

virtual bool MbCurve3D::NearPointProjection	(	const MbCartPoint3D &	pnt,
		double &	t,
		bool	ext,
		MbRect1D *	tRange = `nullptr`
	)		const

virtual

Find the point projection to the curve.

Find the nearest projection of a point on a curve (in the range of the curve) or on its continuation by the given initial approximation. If the parameter ext = true, then also search for a projection on the continuation of the curve. If the range of change of the 'tRange' parameter is specified, then find the projection in the specified range. A range of parameter may not belong to the domain of a curve. The Newton method is used.

Parameters

[in]	pnt	- A given point.
[in,out]	t	- Input - initial approximation, output - parameter of a curve corresponding to the nearest projection.
[in]	ext	- A flag defining whether to seek projection on the extension of the curve.
[in]	tRange	- A range of parameter changing in which the solution should be found.

Returns: Returns true if the found parameter is in a valid range (according to the given ext, tRange parameters), or false - otherwise.

Reimplemented in MbConeSpiral, MbTrimmedCurve3D, MbSurfaceCurve, MbReparamCurve3D, MbPolyline3D, MbPlaneCurve, MbNurbs3D, MbLineSegment3D, MbLine3D, MbHermit3D, MbContourOnSurface, MbContour3D, and MbArc3D.

◆ IsoclinalNewton()

virtual MbeNewtonResult MbCurve3D::IsoclinalNewton	(	const MbVector3D &	dir,
		size_t	iterLimit,
		double &	t
	)		const

virtual

Find isoclines of a curve.

Find the point on a curve where the tangent is parallel to a plane having a normal dir.

Parameters

[in]	dir	- A vector which defines a plane.
[in]	iterLimit	- The maximum number of iterations.
[in,out]	t	- Input - initial approximation, output - parameter of a point of the required tangent.

Returns: The result of the iterative method.

◆ GetIsoclinal()

virtual void MbCurve3D::GetIsoclinal	(	const MbVector3D &	nor,
		SArray< double > &	tIso
	)		const

virtual

Find all isoclines of a curve.

Find the points on a curve where the tangent is parallel to a plane having a normal nor.

Parameters

[in]	nor	- A vector which defines a plane.
[out]	tIso	- An array of parameters of points for the required tangent.

Reimplemented in MbReparamCurve3D.

◆ GetMap()

virtual MbCurve* MbCurve3D::GetMap	(	const MbMatrix3D &	into,
		MbRect1D *	pRegion = `nullptr`,
		VERSION	version = `Math::DefaultMathVersion()`,
		bool *	coincParams = `nullptr`
	)		const

virtual

Construct a planar projection of a piece of a space curve.

Parameters

[in]	into	- The transformation matrix from the global coordinate system into a plane of view.
[in]	pRegion	- A mapped piece of a curve (paramRegion.x = t1, paramRegion.y = t2), by default - the whole curve..
[in]	version	- Version, last by default.
[in,out]	coincParams	- A flag of coincidence between parameterization of initial curve and its projection if coincParams != nullptr then the function tries to create a projection with coincident parameterization if *coincParams = true then parameterization of projection coincides with parameterization of initial curve.

Returns: Two-dimensional projection of a curve

Reimplemented in MbSurfaceIntersectionCurve, MbCharacterCurve3D, MbTrimmedCurve3D, MbSurfaceCurve, MbSilhouetteCurve, MbReparamCurve3D, MbPolyline3D, MbPlaneCurve, MbNurbs3D, MbLineSegment3D, MbLine3D, MbHermit3D, MbCubicSpline3D, MbContourOnSurface, MbContourOnPlane, MbContour3D, MbConeSpiral, MbBezier3D, and MbArc3D.

◆ GetMapPsp()

virtual MbCurve* MbCurve3D::GetMapPsp	(	const MbMatrix3D &	into,
		double	zNear,
		MbRect1D *	pRegion = `nullptr`
	)		const

virtual

Construct a planar projection of a piece of a space curve.

Construct a planar projection of a piece of a space curve for the perspective visualization.

Parameters

[in]	into	- The transformation matrix from the global coordinate system into a plane of view.
[in]	zNear	- The parameter of the perspective visualization which is equal to the distance between the observation point and the plane of view (negative).
[in]	pRegion	- A mapped piece of a curve (paramRegion.x = t1, paramRegion.y = t2), by default - the whole curve..

Returns: Two-dimensional projection of a curve

Reimplemented in MbPolyline3D, MbPlaneCurve, MbLineSegment3D, MbLine3D, and MbArc3D.

◆ GetProjection()

virtual MbCurve* MbCurve3D::GetProjection	(	const MbPlacement3D &	place,
		VERSION	version
	)		const

virtual

Construct a planar projection of a space curve to a plane.

Parameters

[in]	place	- A plane.
[in]	version	- The version of mathematics.

Returns: Two-dimensional projection of a curve

Reimplemented in MbSurfaceIntersectionCurve, and MbContour3D.

◆ IsSpaceNear()

bool MbCurve3D::IsSpaceNear	(	const MbCurve3D &	curve,
		double	eps,
		bool	ext,
		double	devSag = `5.0 *Math::deviateSag`
	)		const

Check whether the two curves are metrically close.

The proximity of curves is defined by equality of their ends and the distance of an arbitrary point of one curve to another curve. Curves may differ parametrically.

Parameters

[in]	curve	- A curve to compare with.
[in]	eps	- The maximum allowed distance between the nearest points of two curves.
[in]	ext	- A flag defines whether the curve 'curve' may be extended when necessary. If ext = true then the curve may be extended.
[in]	devSag	- Maximal value of sag.

Returns: True - if curves are metrically close.

◆ GetCurvatureSpecialPoints()

virtual void MbCurve3D::GetCurvatureSpecialPoints ( std::vector< c3d::DoublePair > & points ) const

virtual

Find all the special points of the curvature function of the curve.

Find all extrema, discontinuity points and inflection points of the curvature function of the curve.

Parameters

[out] points - The array of the found special points of the curvature function.
The first field of each element contains the parameter of the found point.
The second field of each element contains the curvature values at the found points. These values can be of the following types: 1) = 0.0 - inflection point; \ n 2) < 0.0 - curvature value at the minimum point; \ n 3) > 0.0 - the curvature value at the maximum point; \ n Two points are inserted at the curvature discontinuity, to the left and to the right of the discontinuity.
Point with greater curvature is inserted with a plus sign, a point with a lower curvature is inserted with a minus sign.

Reimplemented in MbTrimmedCurve3D, MbSurfaceIntersectionCurve, MbReparamCurve3D, MbContourOnSurface, and MbContour3D.

◆ GetAnalyticalFunctionsBounds()

virtual void MbCurve3D::GetAnalyticalFunctionsBounds ( std::vector< double > & params ) const

virtual

Get the boundaries of the curve sections that are described by one analytical function.

Get the boundaries of the curve sections that are described by one analytical function.
The function was introduced to optimize the implementation of the function MbCurve3D::GetCurvatureSpecialPoints, so as not to calculate the break points.

Parameters

[out] params - Curve parameters in which the analytical function changes.

Reimplemented in MbTrimmedCurve3D, MbSurfaceCurve, MbReparamCurve3D, MbPlaneCurve, MbNurbs3D, MbHermit3D, MbCubicSpline3D, MbContourOnSurface, MbContour3D, and MbBezier3D.

◆ GetLimitPoint() [1/2]

MbCartPoint3D MbCurve3D::GetLimitPoint ( ptrdiff_t number ) const

Calculate the boundary point.

Parameters

[in] number - A number of a boundary point. The value 1 corresponds to the start point of a curve, 2 - to the end point.

Returns: A calculated point.

◆ GetLimitPoint() [2/2]

void MbCurve3D::GetLimitPoint	(	ptrdiff_t	number,
		MbCartPoint3D &	pnt
	)		const

Calculate the boundary point.

Parameters

[in]	number	- A number of a boundary point. The value 1 corresponds to the start point of a curve, 2 - to the end point.
[in,out]	pnt	- A calculated point.

◆ NearestPoints()

MbeNewtonResult NearestPoints	(	const MbCurve3D &	curve1,
		bool	ext1,
		const MbCurve3D &	curve2,
		bool	ext2,
		double &	t1,
		double &	t2,
		double &	dmin
	)

Calculate parameters of the nearest points of two curves.

Calculate parameters of the nearest points of two curves and the distance between these points.

Parameters

[in]	curve1	- Curve 1.
[in]	ext1	- An attribute of search on the extension of the curve 1.
[in]	curve2	- Curve 2.
[in]	ext2	- An attribute of search on the extension of the curve 2.
[in]	t1	- A point parameter of curve 1.
[in]	t2	- A point parameter of curve 2.
[in]	dmin	- The distance between points of curves.

Returns: Return nr_Success (+1) or nr_Special(0) in a case of successful defining, return nr_Failure(-1) in a case of failure.

◆ CurveCrossNewton()

MbeNewtonResult CurveCrossNewton	(	const MbCurve3D &	curve1,
		bool	ext1,
		const MbCurve3D &	curve2,
		bool	ext2,
		double	funcEpsilon,
		size_t	iterLimit,
		double &	t1,
		double &	t2,
		bool	correctNewtonParam = `true`
	)

Definition of parameters of the nearest points of curves.

Iterative definition of parameters of the nearest points of curves by solving an equation by the Newton method with given initial approximations. If curves intersect and initial approximations are close to the intersection point, then parameters of the intersection point will be found.
If curves do not intersect in the region of initial approximations, then there will be found parameters of curves points where tangents to the curves are orthogonal to the segment which connects the found points.

Parameters

[in]	curve1	- Curve 1.
[in]	ext1	- An attribute of search on the extension of the curve 1.
[in]	curve2	- Curve 2.
[in]	ext2	- An attribute of search on the extension of the curve 2.
[in]	funcEpsilon	- The minimal tolerance of the distance between curves intersection points.
[in]	iterLimit	- The maximum number of iterations.
[in,out]	t1	- Parameter of the curve 1 for the intersection point (the initial approximation at input).
[in,out]	t2	- Parameter of the curve 2 for the intersection point (the initial approximation at input).
[in]	correctNewtonParam	- Modify current parameter changes by previous parameter changes.

Returns: Error code: in a case of successful defining nr_Success (+1), nr_Special(0) or nr_Failure(-1) - in a case of failure.

◆ CalculatePolygon() [2/2]

void CalculatePolygon	(	const MbCurve3D &	curve,
		const MbStepData &	stepData,
		std::vector< std::pair< double, MbCartPoint3D > > &	paramPoints
	)

Calculate polygon points of curve.

Parameters

[in]	curve	- Curve.
[in]	stepData	- Data for step calculation.
[out]	paramPoints	- Array of parameters and points.

◆ Explore() [3/3]

virtual void MbFunction::Explore	(	double &	t,
		bool	ext,
		double &	val,
		double &	fir,
		double *	sec,
		double *	thr
	)		const

virtual

Calculate value and derivatives of object for given parameter.

Values of point and derivatives are calculated on parameter area and on extended axis.

Parameters

[in]	t	- Parameter.
[in]	ext	- On parameters area (false), on extended axis (true).
[out]	val	- Value.
[out]	fir	- Derivative with respect to t.
[out]	sec	- Second derivative with respect to t, if not nullptr.
[out]	thr	- Third derivative with respect to t, if not nullptr.

Reimplemented in MbSinusFunction, MbServeFunction, MbPowerFunction, MbNurbsFunction, MbMonoSmoothFunction, MbLineFunction, MbCurveCoordinate, MbCubicSplineFunction, MbCubicFunction, MbConstFunction, MbCompositeFunction, MdAnalyticalFunction, and MdCharacterFunction.

Classes

Functions

Functions for working inside and outside the curve's domain.

Functions for curve domain description

Functions for working in the curve's domain.\n

Functions for working inside and outside the curve's domain\n

Function of moving by curve

Common function of curve.

Common functions

Detailed Description

Function Documentation

◆ TrimContour()

◆ Explore() [1/3]

◆ IsClosed()

◆ IsPeriodic()

◆ PointOn()

◆ _PointOn()

◆ Explore() [2/3]

◆ FastApproxExplore()

◆ Step()

◆ DeviationStep()

◆ MetricStep()

◆ CurveStep()

◆ NurbsCurve()

◆ Trimmed() [1/2]

◆ Trimmed() [2/2]

◆ CalculateLength()

◆ DistanceAlong()

◆ ChangeCarrierBorne()

◆ CalculatePolygon() [1/2]

◆ PointProjectionNewton()

◆ NearPointProjection()

◆ IsoclinalNewton()

◆ GetIsoclinal()

◆ GetMap()

◆ GetMapPsp()

◆ GetProjection()

◆ IsSpaceNear()

◆ GetCurvatureSpecialPoints()

◆ GetAnalyticalFunctionsBounds()

◆ GetLimitPoint() [1/2]

◆ GetLimitPoint() [2/2]

◆ NearestPoints()

◆ CurveCrossNewton()

◆ CalculatePolygon() [2/2]

◆ Explore() [3/3]